Lesson 17 · The circle shape and its bounding box

The circle shape and its bounding box

A body needs a shape to collide. The simplest is a circle, and the cheapest thing you can ask of any shape is its axis-aligned bounding box. Today you build both.

The goal

Define a circle shape and compute its axis-aligned bounding box around a center.

Start here - the target

TO DO

Scenario: The bounding box of a circle

Givena circle of radius 2 centered at {5, 5}

Whenits axis-aligned bounding box is computed

Thenthe box has Min {3, 3} and Max {7, 7}

Anda circle of radius 1 at {0, 0} has Min {-1, -1} and Max {1, 1}

Background

A circle is the friendliest shape in a physics engine - it is the same from every angle, so it has no rotation to worry about, and its collision tests are pure distance checks. All it needs is a radius; its center is wherever the body sits. Define the Circle type now, and it becomes the first thing a body can actually collide with.

Every shape also needs to report an axis-aligned bounding box (AABB): the smallest upright rectangle that fully contains it, described by its minimum and maximum corners. For a circle that is simply the center plus and minus the radius in each direction. Bounding boxes are what the broadphase will use later to reject pairs that cannot possibly be touching, cheaply, before running the exact test - so giving every shape a Bounds is the foundation of making collision detection fast.

Make it work

type AABB struct{ Min, Max Vec2 }
type Circle struct{ Radius float64 }
// the box just fits the circle: center plus and minus the radius
func (c Circle) Bounds(center Vec2) AABB {
  r := Vec2{c.Radius, c.Radius}
  return AABB{Min: Sub(center, r), Max: Add(center, r)}
}

CheckpointDONE

A circle knows its bounding box. Commit and stop here.